Heat water and sugar in a saucepan over medium-high heat until sugar has dissolved, stirring occasionally. Allow to cool. Place watermelon in a liquidiser or food processor. Blend until smooth. Whisk watermelon, lime juice and syrup together in a large bowl. Cover and chill in the fridge.
Pour the chilled mixture into an ice cream maker and freeze according to manufacturer's directions. Transfer sorbet to a 1- or 2-litre lidded plastic container; cover surface with cling film and seal. For best results, sorbet should ripen in the freezer for at least 2 hours or overnight.